Group Scheduling and Due Date Assignment Without Restriction on a Single Machine

We consider a single machine scheduling problem in which the scheduler decides optimal due dates for different jobs under a group technology environment, in which the jobs are classified into groups in advance due to their production similarities, and jobs in the same group are required to be processed consecutively to achieve efficiency of high-volume production. The goal is to determine an optimal job schedule together with a due date assignment strategy to minimize an objective function that includes earliness, tardiness, due date assignment and flow time costs. The due date assignment is without restriction, that is, it is allowed to assign different due dates to jobs within one group. We present structural results that fully characterize the optimal schedule, and give an optimal O(n log n) time algorithm for this problem.